In a short-channel device or in a nonuniformly doped (laterally) MOSFET, may vary along the channel length direction from the source to drain. Generalize the expression in Exercise 4.9 and show that
is not a strong function of11'” the exponential factor dominates. This implies that the subthreshold current is controlled by the point of highest barrier (lowest V's) in the channel. It also implies that the channel length factor entering the subthreshold current expression is different from the effective channel length defined by the linear region characteristics, Eq. (4.61).
Show that in the subthreshold region and when the drain bias is low, Eq. (3.12) leads to Eq.(4.51):